miles formulae for boolean models observed on lattices

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ID: 225900
2011
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Abstract
The densities of the intrinsic volumes – in 3D the volume density, surface density, the density of the integral of the mean curvature and the density of the Euler number – are a very useful collection of geometric characteristics of random sets. Combining integral and digital geometry we develop a method for efficient and simultaneous calculation of the intrinsic volumes of random sets observed in binary images in arbitrary dimensions. We consider isotropic and reflection invariant Boolean models sampled on homogeneous lattices and compute the expectations of the estimators of the intrinsic volumes. It turns out that the estimator for the surface density is proved to be asymptotically unbiased and thusmultigrid convergent for Boolean models with convex grains. The asymptotic bias of the estimators for the densities of the integral of the mean curvature and of the Euler number is assessed for Boolean models of balls of random diameters. Miles formulae with corresponding correction terms are derived for the 3D case.
Reference Key
ohser2011imagemiles Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Joachim Ohser;Werner Nagel;Katja Schladitz
Journal archives of toxicology
Year 2011
DOI
10.5566/ias.v28.p77-92
URL
http://www.ias-iss.org/ojs/IAS/article/view/851
Keywords
image analysis

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